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Int J Adv Manuf Technol (1999) 15:171181 1999 Springer-Verlag London LimitedDevelopment of Automated Fixture Planning SystemsW. Ma, J. Li and Y. RongDepartment of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USAFixturing is an important manufacturing activity. The computer-aided fixture design technique is being rapidly developed toreduce the lead time involved in manufacturing planning. Anautomatedfixtureconfigurationdesignsystemhasbeendeveloped to select automatically modular fixture componentsand place them in position with satisfactory assembly relation-ships. In this paper, an automated fixturing planning systemis presented in which fixturing surfaces and points are auto-matically determined based on workpiece geometry and oper-ational information. Fixturing surface accessibility, featureaccuracy, and fixturing stability are the main concerns in thefixture planning. The system development, the fixture planningdecisionprocedure,andanimplementationexamplearepresented in the paper.Keywords: Accuracy; Clamping; Fixture planning; Locating1.IntroductionFixturing is an important manufacturing activity in the pro-duction cycle. A computer-aided (or automated) fixture design(CAFD) technique has been developed as part of CAD/CAMintegration 1. The development of CAFD contributes to thereduction of manufacturing lead time, the optimisation of manu-facturing operations, and the verification of manufacturing pro-cess designs 2. CAFD plays an important role in flexiblemanufacturing systems (FMS) and computer-integrated manu-facturing systems (CIMS) 3.Figure 1 outlines the activities for fixture design in manufac-turing systems which include three major aspects: set-up plan-ning, fixture planning, and fixture configuration design 4. Theobjective of set-up planning is to determine the number of set-ups, the position and orientation of the workpiece in each set-up, and also the machining surfaces in each set-up. Fixtureplanning determines the locating and clamping points on work-piece surfaces. The task of fixture configuration design is toselect fixture components and place them into a final configur-Correspondence and offprint requests to: Dr Kevin Rong, Departmentof Mechanical Engineering, Worcester Polytechnic Institute, Worcester,MA 01609-2280, USA. E-mail: rongKFig. 1. Fixture design in manufacturing systems.ation to fulfil the functions of locating and clamping theworkpiece. An automated modular fixture configuration designsystem has been developed in which, when fixturing surfacesand points are selected on the workpiece model, fixture unitsare automatically generated and placed into position with theassistance of fixture component assembly relationships 4,5.This paper deals with fixture planning when the fixturingsurfacesandpositionsontheworkpieceareselectedautomatically.Previous papers on fixture design analysis have been pub-lished, but a comprehensive fixture planning system which canbe used to generate fixture plans for industrial applications hasnot been developed. Previous work includes: a method for theautomated determination of fixture location and clampingderived from a mathematical model 6; an algorithm for theselection of locating and clamping positions which provide themaximum mechanical leverage 7; kinematic analysis basedfixture planning 8,9; a fixturing grade and dependency gradebased fixturability analysis 10; automated selection of set-ups172W. Ma and Y. Rongwith consideration of tolerance factors of orientation errors infixture design 11, and finally a geometric analysis based 2Dfixture planning system 12. In our previous research, fixturingfeatures 13, fixturing accuracy 14,15, geometric constraints16, and fixturing surface accessibility 17 have been studied.A framework has been developed for set-up planning andfixture design 18.In this paper, an automated fixture planning system, Fix-Planning, is presented where fixturing surfaces and points aredetermined when the workpiece model and set-up planninginformation is input to the system.2.Basic Requirements of FixturePlanningIn engineering practice, fixture planning is governed by anumber of factors, including workpiece geometric informationand tolerance; set-up planning information such as machiningfeatures, the machine tool and cutting tools to be used in eachset-up; initial and resulting forms of the workpiece in eachset-up; and available fixture components. To ensure that thefixture can hold the workpiece in an acceptable position sothat the manufacturing process can be carried out according tothe design specifications, the following conditions should besatisfied for a feasible fixture plan.1. The degrees of freedom (DOF) of the workpiece are totallyconstrained when the workpiece is located.2. Machining accuracy specifications can be ensured in thecurrent set-up.3. Fixture design is stable to resist any effects of externalforce and torque.4. Fixturing surfaces and points can be accessed easily byavailable fixture components.5. There is no interference between the workpiece and thefixture, and between the cutter tool and the fixture.In this investigation, we focus on the first four requirements.Fixture planning is carried out based on the following consider-ations:1. Although the workpiece geometry can be complex in indus-trial production, in most fixture designs, planar and cylindri-cal surfaces (internal and external) are used as the locatingand clamping surfaces because of the ease of access andmeasurement of these features when the workpiece is fixed.In this investigation, planar and cylindrical surfaces are usedin fixture planning.2. Many CNC machines, especially machining centres, can beused to perform various operations within one set-up. Inmost cases, the cutting-tool axis of the machine tool isfixed. When considering fixturing stability, the locating sur-faces are preferably those with normal directions oppositeto, or perpendicular to, the cutting-tool axis. For clampingfeatures, the normal directions should be in line with, orperpendicular to, the cutting-tool axis, because, in fixturedesign, clamping forces should be against locators.3. For the surfaces to be machined, there should exist datumsurfaces which serve as position and orientation referencesfrom which other dimensions and tolerances are measured.In fixture planning, surfaces with high accuracy gradesshould be selected preferentially as locating surfaces so thatthe inherited machining error is minimised and the requiredtolerances of the machining features are easily attained.4. In fixture planning, more than one workpiece surface mustbe selected for the locating and clamping surfaces forrestricting the DOF of the workpiece in a set-up. Therefore,besides the conditions for individual surfaces, the combi-nation status of the available locating surfaces is alsoimportant for the accurate location of the workpiece.5. Since the locators and clamps are in contact with theworkpiece, the distribution of fixturing points plays a criticalrole in ensuring fixturing stability.6. For a feasible fixture design, the fixturing surfaces must beaccessible to the fixture components. The usable (effective)area of the fixturing surface should be large enough toaccommodate the functional surfaces of the locators andclamps. Besides considering a fixturing surface, the accessi-bility of potential fixturing points on the surface is alsoimportant for the determination of the final fixturing pointdistribution.3.Fixturing SurfacesThe concept of features has been widely used in design andmanufacturing. A workpiece to be machined can be viewed asa combination of features such as planes, steps, pockets, slots,and holes. In a particular operation set-up, features used forfixturing the workpiece can be defined as fixturing features orfixturing surfaces. In practice, most fixturing features are planarand cylindrical surfaces. According to the fixturing functions,the fixturing surfaces can be classified into locating, clamping,and supporting features. Unlike design and manufacturing fea-tures, fixturing surfaces are orientation-dependent. They do notplay the same role throughout the manufacturing processes. Aset of surfaces may serve as fixturing surfaces in a set-up, butmay not be used for fixturing or have different fixturingfunctions in another set-up.The concept of fixturing features allows the fixturing require-ments to be associated with the workpiece geometry. Featureinformation in a feature-based workpiece model can also beused directly for fixture design purposes. For manufacturingfeatures, the information necessary for describing a fixturingfeature contains geometric and non-geometric aspects. Theformer includes feature type, shape and dimensional parameters,and position and orientation of the workpiece. The latterincludes the surface finish, accuracy level and relationshipswith machining features, and surface accessibility.3.1Discretisation of Fixturing SurfacesIn most fixture designs, the fixturing features, especially thelocating surfaces, are planar and cylindrical surfaces. In ordertoevaluatefixturingsurfaceaccessibilityanddeterminelocating/clamping points on fixturing surfaces, a candidate fix-turing surface is sampled into grid-arrayed discrete points withDevelopment of Automated Fixture Planning Systems173equal interval T. If T is small enough, the discrete samplepoints will be almost continuous.In order to make the sampling algorithm generic, an outer-bounding rectangle on the surface is used as the samplingregion. Since in most cases, the primary locating surface isperpendicular to the other locating surfaces, especially in modu-lar fixture designs, the fixturing surfaces are considered asbottom-locating, top-clamping, side-locating, and side-clampingsurfaces. For a bottom-locating/top-clamping surface with anormal Z (or 2Z) direction, two edges of the outer-boundingrectangle must be parallel to the X-axis and two other edgesparallel to the Y-axis. For a side-locating/clamping surface,there must be two edges parallel to the Z-axis, while the othertwo edges must be perpendicular to the first two edges. Figure2 shows an example of sampled candidate fixturing surfaceswith the outer-bounding rectangle. With the assumption thatthe Z-axis is normal to the surface in the surface local coordi-nate system, the points within the outer-bounding rectangle canbe represented as:x = Xmin+ T u,u = 1, 2, %, Nuy = Ymin+ T v,v = 1, 2, %, Nv(1)where Nuand Nvare the numbers of points in the X- and Y-directions, respectively, which are: Nu= int (Xmax2 Xmin)/Tand Nv= int Ymax2 Ymin)/T.3.2Fixturing Surface AccessibilityFixturing surface accessibility is a measure of whether a candi-date fixturing surface is accessible to a regular fixture compo-nent. Three major factors must be taken into account:1. The geometry of the fixturing surface which involves theeffective area and shape of the surface.2. Possible obstruction of the workpiece geometry along thenormal direction and/or around the geometric region of thefixturing surface.3. The size and shape of the functional fixture components.In practical situations, it is possible that a planar surface ofthe workpiece has a complex shape and has a full/partialobstruction along its normal direction and/or around its geo-Fig. 2. Sampling of a candidate fixturing surface with an outer-bound-ing rectangle.metric region. It is thus required that the accessibility modelshould comprehensively reflect these facts so that a reasonablycomparable accessibility value can be applied for every candi-date fixturing surface.The surface accessibility is defined as a statistical valuebased on the point accessibility (PA) of every valid samplepoint on the surface, where PA consists of two parts: the pointself individual accessibility (SIA) and the point neighbourrelated accessibility (NRA). The SIA corresponds mainly to theisolated accessibility of the fixturing point, whereas the NRAreflects the extended accessibility of the fixturing point.The SIA of a sample point is defined on the basis of threeattribute tags. The tag s1is used to indicate whether the squaretest grid with its centre at the current sample point is inside,on, or outside the outer-loop of the fixturing surface. Threediscrete values are assigned to represent its status, i.e. 0, 1,and 2, respectively.If there exists obstructive workpiece geometry in the surfacenormal direction or surrounding the sample point, this affectsthe surface accessibility at the sample point. For example, asshown in Fig. 3(a), on a candidate bottom-locating surface ofa workpiece, sample point p1is not accessible because of theobstructive geometry of the workpiece along the bottom-locat-ing direction, and p2is not accessible either because of theobstructions surrounding it. To evaluate automatically whetheran obstruction exists in the surface normal direction, a virtualvolume is generated by extruding the square test grid to asolid entity in the surface normal direction. By employing atechnique for detecting the interference between two solidentities, the obstruction can be identified, as shown in Fig.3(b). The extruding method is a little different for the squareFig. 3. Obstruction checking at virtual sample points on a bottom-locating surface. (Kpimeans the extrusion is carried out at point pialong its accessible direction.)174W. Ma and Y. Rongtest grid on the side-locating/clamping surface, where thesquare test grid is first stretched along the bottom-locatingdirection, and then the stretched grid is extruded along theside-locating/clamping direction as illustrated in Fig. 4. Theattribute tag s2is used for recording the result of obstructionchecking at a sample point. When such an obstruction isdetected, s2= 1, otherwise, s2= 0.If the test grid at the sample point is found to be notobstructed, its individual accessibility is largely dependent onthe contact area between the test surface and the fixturecomponents, which is represented by the attribute tag s3. Thedefinition of s3iss3=Area1T2,s3P 0, 1(2)where AreaIis the contact area and T is the edge length ofthe test grid.On the basis of above three attribute tags, the SIA of asample point pu,vcan be given by a numerical value accordingto the following rules:if s1= OutsideOuterLoop, SIA = 21 (inaccessible);if s1 OutsideOuterLoop AND s2= Obstructed, SIA =2 1 (inaccessible);if bottom-locating/top-clamping AND S1 OutsideOut-erLoop AND s2= NotObstructed, SIA = s3;Fig. 4. Obstruction checking at sample points on a side-locating/ clamp-ing surface.if side-locating/clamping AND s1 OutsideOuterLoopAND s2= NotObstructed, SIA = 0.5vs3;where v reflects the height effect of the point in sidelocating/clamping.The accessibility in the surrounding area of the sample pointalso affects the accessibility of the point. On a fixturing surface,the positional relationship between the current sample pointand all the neighbouring sample points can be represented bya 3 3 map where Pcis the current sample point with adiscrete position of (u, v), P1| P8are 8-neighbour samplepoints, and their locations are all labelled in Fig. 5. The NRAat sample point pu,vcan be calculated using the equation:NRA(u, v) =O8k=1Fk8(3)where Fkis the related-access factor of kth neighbour, whichcan be determined based on the SIA as well as its measure(s1, s2, s3).For bottom-locating/top-clamping,F9k=521,s2(pk) = 10,s1(pk) = 2and s2(pk) = 0IA(pk), s1(pk) 2 and s2(pk) = 0(4)Fk=5F9k,k = 1, 3, 5, 7F9k,k = 2, 4, 6, 8, F9k21$ 0and F9k+1$ 021, k = 2, 4, 6, 8, F9k21= 2 1 or F9k+1= 2 1(5)For side-locating/clamping,F9k=521,s2(pk) = 1, k = 1, 5, 6, 820.5,s2(pk) = 1, k = 2, 3, 40,s1(pk) = 2and s2(pk) = 0SIA(Pk), s1(pk) 2 and s2(pk) = 0(6)Fk=5F9k,k = 1, 3, 5, 6, 7, 8F9k,k = 2, 4,F93$ 020.5, k = 2, 4,F93= 20.5(7)For a valid sample point, once the SIA and NRA are obtained,the PA can also be calculated according to the equation:Fig. 5. 3 3 position map of current point Pcand 8-neighbour samplepoints P1| P8.Development of Automated Fixture Planning Systems175PA = SIA + NRA,if PA , 0,then PA = 0(8)From the definitions of SIA and NRA, SIA is in the rangeof 0 | 1 and NRA is in the range of 21|1. Therefore, PAmust be in the range of 21|2. When the value of PA is lessthan zero, the sample point is severely obstructed and is nota feasible fixturing point. The overall accessibility (OA) of thefixturing surface is defined as the sum of the PA values at allvalid sample points, i.e.,OA =ONvalidPAu,v,sample point pu,vis tested valid(9)As OA is statistically measured by the overall effect of theaccessibility of the sample points on the surface, the infor-mation about the effective area and shape complexity of thesurface is represented in the model. Generally, the modelsatisfies the criterion that the surface with the larger OA ismore accessible than the one with the smaller OA.3.3Generalised Accuracy of the Fixturing FeaturesOne of the most important tasks for fixture planing is toguarantee that the tolerance requirements are met when theworkpiece is machined. The accuracy of features can be charac-terised by their tolerance and surface finish, and the tolerancebetween features. Generally, the tolerance of features can beclassified into two types: dimensional tolerance and geometrictolerance. The magnitude of the dimensional tolerance mayexpress the relationship between two features on the workpiece.If there is a feature with a tight dimensional tolerance withrespect to a machining feature, this implies that the featuremay be used potentially as an operational datum, i.e. a locatingsurface in the set-up. Based on whether a datum feature isneeded, the geometric tolerance can be further divided intoform tolerance and positional/orientation tolerance. The formtolerance is associated only with the feature itself, whichspecifies the allowable geometric variation of individual fea-tures. The form tolerance, e.g. surface finish, of a featureaffects the suitability of the feature to be the fixturing datum.The positional/orientation tolerance is of the same importanceas the dimensional tolerance for fixture planning since it alsorepresents a relationship between features. In order to evaluatethe accuracy of a feature and use it efficiently in fixtureplanning, a generalised feature accuracy grade is applied inthis investigation, which is defined as:Tg= (w1Td+ w2Tp) * (w3Tf+ w4Tr)(10)where Td, Tpand Tfare the dimensional tolerance grade,positional tolerance grade and form tolerance grade, respect-ively; Tris the tolerance grade equivalent to the surface finishof the feature. w1, w2, w3, and w4are the weight factors. Themultiple operation “*” represents a dominant relationship wherea zero value can contribute to the final result, while theoperation “+” represents a relatively weak relationship withpreferences. Td, Tp, Tf, and Trcan be obtained by applying thealgorithms described in 11,18.4.Development of Automated FixturePlanning SystemsAn overview of the automated fixture planning system is shownin Fig. 6. The procedure for fixture planning can be dividedinto five stages, i.e. input, analysis, planning, verification, andoutput. The input data includes a workpiece CAD modelcontaining the geometric and tolerance information of thefeatures of the workpiece, and set-up planning informationincluding the features to be machined and the machine tooltype for the specific set-up. The data can be extracted eitherfrom a CAD database or entered interactively by the user ina CAD system.Analysis involves the extraction of the candidate fixturingfeatures with related accuracy information and an evaluationof the accessibility of the fixturing features. In this study, planarand cylindrical surfaces are considered for fixturing purposes.The task of planning is to determine automatically theprimarylocatingdirectionandtoselecttheoptimallocating/clamping surfaces and points in the current set-up.Algorithms are developed for the planning of the bottom (top)and side locating/clamping arrangements.Accurate location is the major contributor in ensuring themachiningaccuracyoftheworkpiece.Oncethelocating/clamping scheme is determined, the fixture units corre-sponding to the fixturing points can be generated by usingthe fixture configuration design system (Fix-Des) developedpreviously 19. A comprehensive program has been developedFig. 6. The procedure of fixture planning.176W. Ma and Y. Rongto analyse the final fixture design in terms of the cumulativetolerances of fixture components and the effects on work-piece accuracy.Theoutputofthefixtureplanningisthefixturingsurfaces/points in the format of a fixture plan which can beused in fixture configuration design. Although the fixture planis generated based on some optimisation rules, alternativefixture plans are also provided for further optimisation oruser confirmation.4.1Determination of Primary Locating DirectionIn fixture design, there are usually three locating referencesurfaces which determine the position and orientation of theworkpiece. The primary locating surface is the major locatingdatum for determining the spatial position and orientation ofthe workpiece in the current set-up and constraining at leastthree DOF of the workpiece. The primary locating surface isperpendicular to the other locating surfaces, which is especiallytrue when modular fixturing systems are used. In the generalcase, the primary locating surface could be a single plane orseveral planes in the same direction with the same or differentheights. The normal direction of the primary locating surface,called the primary locating direction, needs to be determinedfirst in fixture planning. It should be parallel or perpendicularto the cutting tool axis of the machine tool. Assume that thetool axis is Vt= (Vx, Vy, Vz). The surfaces with normaldirections parallel or perpendicular to the tool axis are extractedfrom the workpiece model. They are grouped as follows:Sfn= fi(Vi, Tgi, Ai) u Vi Vtor Vi= 2Vt, Nf. i(11). 0,Ns. n . 1where Sfndescribes a group of surfaces with a normal directionin the primary locating direction; fi(Vi, Tgi, Ai) represents afeature with a normal vector Vi, a generalised accuracy gradeTgi, and a usable (effective) area Ai; Nfis the number of thefeatures in the group; and Nsis the number of feature groups.If the primary locating direction is selected as Vl(Vlx, Vly,Vlz) and Vl P Vi, the following index is used to identify Vlwith a priority order:InFVl = maxWA* SAn/maxSA + WT1* STn/maxST, Ns(12). n . 1where WAand WT1are the weight factors for surface area andaccuracy, respectively. SAn=ONfj=1Aj, STn=ONfj=1Tgj, maxSA is themaximum area in the group, maxST is the maximum value ofthe generalised feature accuracy grade in the group. Once theInFVl is obtained, the normal vector corresponding to the InFVlis selected as the primary locating direction.4.2Planning for Bottom Locating and TopClampingThe task of fixture planning in this stage is to determine thesurfaces suitable for primary location and the distribution ofthe locating points on the surface, as well as the clampingsurfaces and points corresponding to the primary location, asshown in Fig. 7.The set of the candidate primary locating surface can berepresented as:LV = fi(Vi, Tgi, Ci) u Vi= 2Vl,Nf. i . 0(13)where fj(Vi, Tgi, Ci) is a feature with a normal vector Vi, ageneralised accuracy Tgi, and contours Cicharacterised by linesand arcs, Nfis the number of features in the set.When more than one plane is involved, the planes areprojected along the primary locating direction to form a virtualplane surface which is represented by its boundary entitiessuch as line segments and arcs. As the surface is sampled atdiscrete points, an outer-bounding region is generated in thevirtual plane. As locating points cannot be very close to theouter edges of the workpiece, the size of the rectangular regionis reduced by moving the boundary toward its centre with T.The projection of final locating points will be in this newregion. However, since some points may be outside the surfaceboundary, a standard algorithm is employed for detectingwhether a point is in the specific region.In the primary locating direction, three points (or equivalent)must be selected to constrain three DOF. The three points canbe used to construct a triangle and the centre of workpiecegravity should be located inside the triangle in order to guaran-tee locating stability. The optimal locating points are selectedbased on the following factors:1. The area of the triangle should be as large as possible. Itis calculated as:TA = (S(S2l1) (S2l2) (S2l3)(14)where S = 0.5 * (l1 + l2 + l3), and l1, l2, l3 are the edgelengths of the triangle.Fig. 7. A procedure of fixture planning in the vertical direction.Development of Automated Fixture Planning Systems1772. The distance from thecentre of gravity of the workpieceto the three edges of the triangle should be as large aspossible, It is calculated as:TL =O3i=1Di(15)where Di is the distance from ith edge of the triangle tothe workpiece centre of gravity.3. The generalised accuracy of the planes in which locatingpoints locate should be as high as possible (the tolerancevalue is as small as possible). It is calculated as:TT =O3i=1Tgi(16)where Tgiis the generalised accuracy grade of the plane inwhich the locating point Pilocates.4. The accessibility of the three locating points should be aslarge as possible. It is calculated as:TC = minAcci, Accj, Acck(17)where Acci, Accj, Acckare the accessibility values of thethree locating points.5. The locating height equalisation should be as uniform aspossible. It is evaluated as:TH =51, if zi zj zk2, if, zi= zjor zi= zkor zj= zk3, if zi= zj= zk(18)When the values of the above factors are obtained, thefollowing index is used to identify the optimal locating points,which has the maximum value:InFPl = WS* (TA/maxTA + TL/maxTL)(19)+ WT2* TT/maxTT + WC1* TCi+ WH* TH/3where WS, WT2, WC1and WHare the weight factors forfixturing stability, accuracy, accessibility, and uniform height,respectively; and maxTA, maxTL, and maxTT are the normalis-ation factors for all candidate vertical locating planes.Once the final locating points are determined, the locatingsurfaces corresponding to the three locating points are obtained.It should be noted that by using this procedure one or moreplanes may be selected as primary locating plane candidates.Selection of the clamping type is related mainly to thedirection of the machining force and the surfaces availablefor placing clamping devices. The top clamping surfaces aredetermined based on the following criteria:1. The surface is opposite to the bottom locating surfaces.2. The surface is the machining surface in the current set-up.3. There is an overlap area if the surface is projected into thebottom locating triangle region.4. The surface is easily accessible by the clamp (e.g. it has ahigh value of accessibility).Once the clamping surface is determined, the optimal clamp-ing point is selected so that the clamping force is in thedirection against one of the bottom locators or inside thebottom locating triangle.After the steps stated above, all the fixture plans available forbottom locating and top clamping are generated and recordedsequentially with priority determined by InFPl. Each fixtureplan file contains fixturing information such as fixturing func-tions, locating/clamping surface IDs, and the coordinates ofthe locating/clamping points.4.3Side Locating/Clamping PlanningFixture planning in horizontal directions includes side-locatingand clamping planning. Side locating is to determine the non-primary locating surfaces and points. The most commonmethod of side locating is the standard 3-2-1 locating principle.In this case, side locating planning selects two perpendicularplanes as the secondary and tertiary locating surfaces wherethese planes contain two and one locating points, respectively.This locating scheme is preferred when designing a fixtureconfiguration and controlling locating accuracy because of theindependent constraints in different DOF. However, there aremany cases where it is hard to find such mutually perpendicularlocating planes in fixture design. For a more general situation,cylindrical surfaces and non-perpendicular planes may alsoserve as the locating surfaces and sometimes, the three side-locating points may be distributed on three different surfaces.In this study, general solutions are provided, including thestandard 3-2-1 situation as the priority solution.To select satisfactory side-locating surfaces, the normal direc-tion, generalised accuracy grade, accessibility value, and theshape of the candidate surfaces are taken into account. Theset of features which meets the side-locating requirements canbe expressed as:LH = fi(Vi, Tgi, Acci, Ci) u Vi Vl for planes, Vi/Vl(20)for cylinders Nf. i . 0where fi(Vi, Ti, Acci, Ci) is a feature with a normal vector Vi,a generalised accuracy grade Tgi, an accessibility Acci, andcontour Ci; Nfis the number of features in the set.In order to constrain three DOF remaining from the primarylocating, more than one surface is needed for side locating.As previously stated, besides the condition of individual sur-faces, the combination status of the candidate locating surfacesis also an important factor affecting the locating of the work-piece. For the two kinds of locating features, there are manycombinations which can be used in side locating. The followingis a partial list of the combinations in the preferred order:1. Two planes perpendicular to each other.2. Two planes which are not perpendicular.3. Three planes.4. One plane and one cylindrical surfaces.5. Two cylindrical surfaces.6. One plane and two cylindrical surfaces, as shown in Fig.8. Based on these types of combinations, feature groupscan be constructed and expressed as:178W. Ma and Y. RongFig. 8. The feature combination types. 1. Two perpendicular planes.2. Two non-perpendicular and non-parallel planes. 3. Three non-perpendicular and non-parallel planes. 4. One plane and one cylindricalsurface. 5. Two cylindrical surfaces. 6. One plane and two cylindri-cal surfaces.LHCm= fiu i = 1, 2 or 1, 2, 3, fiP LH,(21)m = 1, 2, %, Nmwhere fiis a selected feature in the group and Nmis thenumber of feature groups.Each feature group contains two or three features. Thecriteria used for evaluating the feature group includes:1. Feature combination status. A weight factor, HF, is assignedto the different types of combination of locating surfaces,which is the most preferred if the feature group comprisestwo perpendicular planes and which is the least preferred ifthe feature group is comprised of three cylindrical surfaces;2. Generalised accuracy grade of the feature group. The gener-alised feature accuracy grade is considered for all the sur-faces in the group, HT = STi, where Tiis the generalisedaccuracy grade of the surface i in the feature group, and i= 1, 2, and 3.3. Accessibility value of the feature group. Accessibility ofeach surface in the group is considered, HC = minAcciu i= 1, 2, or 3, where Acci, is the accessibility value of thefeature in the candidate horizontal locating surface group.The following index is used to identify the optimal locatingsurface group when the values of the above factors areobtained.InFHl = HF + WT3* HTi/maxHT + WC2* HCi, Ns. i . 1(22)where WT3and WC2are the weight factors for surface accuracyand accessibility, respectively, and maxHT is a normalisationfactor of feature accuracy.When the candidate locating surfaces are classified intogroups, the locating height is determined. It is desired that allthe side locators, as well as the clamps, are placed at anidentical height, or the difference of the side-fixturing pointheights is minimum.Fig. 9. Workpiece model and intersection plane for side locating.Once the locating height is determined, the available locatingregion in the locating surfaces become 2D lines and arcs orcircles. Those 2D locating “regions” can be extracted directlyfrom the workpiece CAD model. Figure 9 shows an exampleof the cross section at the locating height. The positions ofthe locating points on the 2D line segments are determined,based on the different surface status and point accessibility.Two conditions must be satisfied for a feasible solution forside-locating planning 16. The first one is that the normaldirections of the locating surfaces cannot all be parallel, whichis ensured in the feature grouping process. The second one isthat the normal directions from the three locating points cannotmeet at one point, which would give an uncertain location ofthe workpiece.For fixturing stability, the side clamps should be applied tosurfaces which are opposite to the locating surfaces. A completesolution has been developed for determining the side-clampingsurfaces and feasible regions of the clamping points 20.Figure 10 shows the planning procedure of side locating/clamping.Development of Automated Fixture Planning Systems179Fig. 10. A procedure of fixture planning in a horizontal direction.5.Implementation Example andConclusionA fixture planning system, Fix-Planning, is developed, whichis integrated with a CAD system and an automated fixtureconfiguration system, Fix-Des. The CAD system is used as aplatform to provide the system with the input informationnecessary for fixture planning, and Fix-Des is used for generat-ing the fixture configuration design using the output from Fix-Planning. Figure 11 shows the main system menu showingeight functional modules. SysSetup is used to initialise thesystem before performing the planning tasks. An example ofsystem initialisation is shown in Fig. 12 where the customisedplanning conditions are set-up, such as the clamping type, theminimum size of locators and the minimum placement heightof locators in horizontal locations, and the priority sequenceTable 1. Results of accessibility analysis (BL bottom-locating; SL side-locating; SC side-clamping; TC top-clamping).Face-idNormal directionAreaFunctionValidOAF1(0, 21, 0)6095.04SL/SCYes1.312395F8(1, 0, 0)1900SL/SCNoN/AF10(0, 1, 0)2322.58SL/SCNoN.AF11(21, 0, 0)6464.19SL/SCYes6.983632F12(1, 0, 0)5126.26SL/SCYes4.819779F13(0, 0, 21)3462.37BLYes0.875000F14(0, 1, 0)563.77SL/SCNoN/AF15(1, 0, 0)614.14SL/SCNoN/AF16(0, 21, 0)563.77SL/SCNoN/AF17(21, 0, 0)614.14SL/SCNoN/AF18(0, 0, 21)875.73BLNoN/AF23(0, 0, 21)12342.47BLYes16.962994F28(0, 1, 0)3109.46SL/SCYes4.090943F35(0, 1, 0)1008.58SL/SCYes0.967515F36(0.707, 0.707, 0)1996.16SL/SCYes1.743387F38(0, 0, 1)9942.9TCYes19.599906F40(0, 21, 0)3415.2SL/SCYes1.219500F44(0, 1, 0)2322.58SL/SCYes0.579375F59(0, 21, 0)1578.54SL/SCYes2.114299Fig. 11. Overview of the Fix-Planning system.Fig. 12. An example of initialisation of the system.of the major factors which affect the vertical location. File isused to read the workpiece specification from the CAD datab-ase, and to store the fixture plans for fixture configurationdesign. LocatingDir is for determining the workpiece primarylocating direction. Accessibility is for evaluating the accessi-180W. Ma and Y. RongFig. 13. PA values of sample points on a bottom-locating candidatesurface F23. (a) The distribution of sample points on surface F23. (b)PA values of all sample points on F23.bility of fixturing features and points. The algorithms forside- and bottom(top)-locating/clamping are embedded in themodules HorLocating, HorClamping, VerLocating and Ver-Clamping. When fixture planning is completed, the results aredisplayed with priority preference.An example workpiece is shown in Fig. 9(a) where the stepsurface F46 is to be machined. Table 1 shows the results ofthe accessibility evaluation for candidate fixturing surfaces andFig. 13 shows the point accessibility distribution of a candidatebottom-locating surface. The results of fixture planning in thehorizontal and vertical directions are shown in Fig. 14. Theresults may not be unique. Alternative plans are also providedwhen necessary. Figure 15 shows the fixture configurationdesign.As seen in the example, the fixturing surfaces and pointsare automatically selected based on the consideration of mul-tiple factors including feature accuracy, fixturing stability, andfixturing surface accessibility. In the system, the workpiecegeometric information is extracted directly from CAD models,set-up planning information is specified as input, and planarand cylindrical surfaces are considered as fixturing surfaces.Fixturing surface groups are established for vertical and hori-zontal planning. Alternative plans are provided for furtheroptimisation and user confirmation. Fixturing points are alsoautomatically determined, which is the output for fixturingconfiguration designs using the previously developed system,Fig. 14. (a) An example of horizontal locating/clamping. (b) Anexample of vertical locating. (c) An example of vertical clampingcorresponding to vertical locating.Fix-Des.